Conditional Statements: if p then q

Learning Objectives:
1) Interpret sentences as being conditional statements
2) Write the truth table for a conditional in its implication form
3) Use truth tables to see the disjunctive form of a conditional statement as logically equivalent
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This video was created by Dr. Trefor Bazett

[@jbonceu2457]

My thought process for this have always been: -If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT) -If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG) -If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT) -If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT) Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)

[@fallenangelonline3930]

omg this is so helpful, i learn faster this wayyy

[@ahmed_mahrouky]

wow , you are brilliant, thanks

[@ycombinator765]

WOW, You are a genius. Thanks for this so much!

[@h3nry_t122]

I thought if p and q as a promise I promise that: if p happens then q will happen too if p happens -> q happens : True (promise is upheld) if p happens -> NOT(q happens) : False (promise is broken) if NOT(p happens) -> q happens : True (promise is upheld) if NOT(p happens) -> NOT(q happens) : True (promise is upheld) example: I promise that: if you have a dog then it is blue have dog -> color is blue : True have dog -> color is not blue : False have cat -> color is blue : True (original promise about dogs being blue is still True) have cat -> color is red : True (cats being red doesn't affect my promise) just because you have a cat doesn't mean my promise is broken. cause my promise is about DOGS being blue. cats got nothing to do with it.

[@youtubeessentials2996]

🥰😍

[@matalebtube4900]

If I study Hard -- then I will pass == Satisfied with result :) If I study Hard -- then I don't pass == not satisfied with result :( If I don't study hard -- then I pass == F**k Yeah I am satisfied :D I I don't study hard -- then I don't pass == F**k it, I didn't study so I am satisfied with results :) I hope this made better sense, these KZbin videos makes it more complicated sometimes :D

[@sulemanahmed6770]

you are a fucking legend. You helped me so much i was strugling to remember the if then table now i will not forget it. Thanks my g

[@naff9n435]

i knew something like this was similiar to domain and range fungtion. except the x variable where change to Truth varioable.

[@lohitharudra7502]

Helpful🔥

[@leungwallace8552]

Seems like not studying makes us satisfied anyway

[@susanlaime1318]

Thanks, now I remember.

[@Pgonz7821]

Bless my professor literally rushed through this entire topic in two sentences, gotta hate summer classes

[@marciahuell]

Likewise it's been a challenge for me finite maths

[@victordadagaming928]

😢gdgxsfcl❤ggd🎉hdmvl​@@marciahuell

[@victordadagaming928]

Hvzlr

[@stormyheadley764]

This was incredibly helpful. My textbook feels so incredibly over-saturated with unnecessary information and it was overwhelming. The simplicity here and your clear explanation saved my grade this week! Thank you so much!

[@DrTrefor]

Glad it was helpful!

[@rachalvinson-steckley8523]

@@DrTrefor 9

[@senpaixd1346]

My textbook is written by someone who just wanted to fill the book with words without going through the trouble of explaining things

[@TecknoVicking]

What I found ungrateful, is that without the textbook, you wouldn't have come here in the first place to understand. Let's honor the textbook for being (sometimes) way too dense.

[@Mark-sc4bu]

'Vacuous truths' - brilliant! Truth tables were easy right up to the p(false) implies q (true) line, and this has really stumped me. Other videos just say 'memorise the outputs' and failed to explain WHY the outputs were the way they are for conditional statements - memorising was easy but this video really helped me understand the underlying logic - thank you!

[@ShamSham519]

Dude this was so helpful- I'm a visual learner and this is just brilliantly done

[@badwrong]

No such thing as a "visual learner"...

[@makeki7756]

@@badwrong veritasium

[@ShamSham519]

@@badwrong you’re correct that the term “visual learner” isn’t actually a real learning “style”. That being said, I still found the visual format of this video helpful for my comprehension on this subject matter. Take care :)

[@hongminh4963]

@@badwrong If there's no such thing "visual learner," then define it in a new way such that it exists.

[@levinashon22]

@@badwrong Not true 😅 Pun intended 😅

[@300PIVOTMASTER]

Explaining it using the ~p V q logical equivalency really helped me to finally grasp implication. Thanks!

[@Juan-yj2nn]

How is that ~p V q has nothing to do with real life implication?

[@wintutorials2282]

​@@Juan-yj2nn yes it does its kinda hard to explain but p implies q means: First: if p is true, q must be true (p=true IMPLIES that q=true) Second: if p isn't true, p IMPLIES q is also true, no matter what q is. (Think about it: if p isnt true, it's still true that a case where p is true, q is also true) Now what is true in any case here, if p-->q is true? If we look at both rules we find that the statement is always true when q is true or when p is false This gives ~p v q Now is this a coincidence or re they logically the same in any way? Well.. using human language to describe logic is difficult because human language is vague. The words we use to describe logic (if p then q / p implies q / p AND q etc) are ways to emulate the meaning of logic to human language. If the logic is the same, it's the same, in real life, anywhere. It means the same, it is the same in any way same or form. The thing that's different is our emulation of the logic. The word AND, is the closest we'll get to the real "logical meaning". The best way to emulate in human language/think about p --> q in my opinion is like this: --> is a logical operator that evaluates the truth value of a **promise of a theory leading to a conclusion** , where p is the hypothesis and q is the conclusion. Might sound difficult but if to bring it a little closer to human language: think of it like a scientist that promises you that if p is true, then q is true. Whether his promise is held or not determines the truth value . So if p=true leads to q being true, he doesn't break the the promise. If p=true leads to q being false, he breaks his promise: his theory didnt lead to the right conclusion. If p=false (his theory doesnt work) his entire promise isn't broken. It's the PROMISE (and the promise and all the logic, in whatever way you interpret that, what represents the logic of -->). For the promise to hold, the hypothesis being true what makes the conclusion being true a necessity For the promise to hold, the conclusion being false is what makes the hypothesis being false a necessity This is the relation of --> In logic terms: For p--> q to be true: p being true, REQUIRES q to be true (it won't hold when q is false) q being false REQUIRES p to be false (it wont hold if p is true) Hmmm.. so the logic is based on 2 requirements for two situations and all other situations are true it seems. (Just like how the logic of AND is based on 1 requirement: p and q need to be true at the same time) The 2 requirements, things that need to be true at least are: p being false or q being true In other words: ~p v q

[@dearnobitaa]

This is mirrored, are you really left handed!!! Your Voice guides me

[@ivanbenitez567]

I'm currently studying this for university entrance exam here in Mexico, so I came across this chanel. Your explanation is definitely easier than my textbook but I was still confused with some parts of the video so I will have to watch it as many times as needed to get it all. Thanks for the content.

[@Salvation1984]

I was so stumped when I read this in my textbook, I'm prepping for my upcoming math class and want to understand the concepts before class starts. This was VERY helpful! Subscribed!

[@DrTrefor]

Really glad it helped, good luck in your class:)

[@AmandaLaVlog]

Using this to study for the LSAT. Thanks for the video, helps a lot!

[@danielcash1037]

I love a teacher who is enthusiastic and teaches at an understandable speed. Such a good combo. It's so common you only get one of the two.

[@yuriroiter2167]

Thank you, I finally got it looking this and other your videos! I had to develop a bit more resonating with myself explanation though. Hope it will help somebody more as well. :) Say, my (actually yours from another video :)) implication is: If it is a dog, then it is a mammal. Then, my implication is considering a dog (being a mammal) only, not a cat or a table. I agree (It is true) that when it is not a dog (p = false), then it can be anything -- mammal or not mammal (q is true or false). Thus, my implication is TRUE in both cases when it is not a dog -- then everything is all right with my implication, and I AGREE that (not a dog) can be anything. But when it is a dog, then my implication is ONLY TRUE when it is a mammal -- because it is what I specifically imply! Otherwise, my implication is FALSE. I.e. when it is a dog, and it is not a mammal -- then and only then my implication FAILS. Only then my implication is WRONG. CONCLUSION: Implication is FALSE ONLY when it is WRONG! Let's create a new boolean result: WRONG! :))

[@iuseyoutubealot]

loved this explanation

[@rainbowestarz]

I’m teaching truth tables to my students and this video is great!

[@ptree1694]

You're videos are going to be my savior in my discrete mathematics class. My professor is extremely confusing when she's trying to explain pretty much everything. The textbook helped, but there were still some things I needed some clarification on and you explained them perfectly. Thank you so much for taking the time to make these videos.

[@missamal4553]

finally i got the explanation that i want, ur smart and the way u explan is very clear ...thanks a lot

[@majorlookgaming6070]

Thank you for helping my college algebra course make more sense. You rule.

[@DrTrefor]

Thank you so much, really appreciate that!

[@kristianholtedk]

Thank you for explaining the scenarios where the initial statement is false :)

[@mehakverma4195]

7:08 mins worth it :) Thank you so much, Dr. Trefor Bazett

[@deadchannel9624]

this vid has been given to me by the online teacher cuz the quarantine

[@Its.ary1220]

Is this considered a tautology

[@calebus9149]

Thank you so much for this video Dr. Bazett!! I had been spinning my wheels on this Critical Thinking module for the past six hours when I came across this video. Super helpful!! You're definitely getting a sub from me!

[@DrTrefor]

You're very welcome!

[@aruns.g.2799]

Hi Trefor, thanks for this video. Quite a few books that I referred to skip the last two cases completely or gloss over it without going into even a minimal depth. I see you dint skirt the last two cases and in fact your study/pass example put things in better context. I'm taking Logic as a subject in a course on Philosophy and can see where this trouble originates. It lies in the epistemology of different philosophies. The classical Western/Aristotelian ( multi valued logic addresses this gap ) version of truth is True/False , 0/1. However classical /ancient Indian philosophy has a layered or more nuanced version of truth. 7 versions, actually, ranging from True to False! Some of the indeterminate ones are - somehow ( or sometimes) true, somehow ( or sometimes ) untrue, Both true and false ( think Both sides claiming victory in a war!), Neither true nor false.....etc. This layered approach to truth is reality of life and where all confusions, conflicts, distrust, outrage arise. When life is black & white, this works perfectly, but breaks down when things are grey. In short, the real answer to the 2 cases when P is "F" should be "unknown".

[@heyytabi]

This is why i like literature more😭😭😭😭

[@anshulpatil1285]

Thank you So Much Sir 🙌. Your Video Helped me Understand the very thing I was having a doubt in. This one was Precise and Short 👍

[@Rams4ajnsz]

I'm just here because my girlfriend was teaching me this early and I want to take interest in the things she enjoy.. great video now let me go make her happy

[@CalypsoSnail]

Thank goodness for this video, I nearly cried trying to do my geometry homework with no knowledge of what a conventional statement was because my geometry teacher didn't explain what those where to anyone in the class.

[@haha-vm6gi]

You gave me a complete idea and you opened my logic! THANK YOU FOR THIS VIDEO! I needed this , because they taught us this in university, but i didnt understand!!! but now I do! The way you teach is wonderfulllll! thanks again! Greeetings from Turkmenistan

[@DrTrefor]

You're so welcome!

[@zoha1266]

this just made my day like i understand this easily so grateful to you for that

[@younisali2688]

I'm learning from you not only the information but the skill of delivering the information. Thank you for your efforts.

[@DrTrefor]

My pleasure!

[@jenniferbohannon7014]

"if p, then q" example is "if it is a dog (p), then it is blue (q)." This is logically equivalent to "it is either NOT a dog (p) OR it is blue (q)". It kind of makes sense if I think of it like this...

[@montronics8430]

Sir this is so helpful... It really helped me.

[@clue64]

Thank you so much, I couldn't interpret that the statement was based if p was True in all scenarios of the conditional statement.

[@amckeetrades]

I'm currently going through your playlist and this is really helping me study for my midterm. Thanks!

[@DrTrefor]

Best of luck!

[@Airaldi]

I think this will help the most: "If p then q" isnt the same as "If and only if p, then q". "If p then q", only means that when p is true, then q should aswell be true. But it can also happen that p was not the case, but q still be true. We havent discard that possibility, we have just said that, "if p happends to be true, then q is true aswell", but we havent said, "only if p is true, then and only then q can be true aswell".

[@hashemalattas9009]

Ohmagaaaa

[@jaredmartin8944]

Hey Dr. Trefor, you are amazing! Thanks for sharing it.

[@cancelcancel6613]

It's fun to learn when Marc Gasol is the one teaching you

[@maliksaifaminoden9785]

Lol. I also noticed that

[@sotha8203]

Cool! So in essence, you cannot derive a false conclusion from a true assumption. I'm so glad I found this channel. The way you break down and explain concepts reminds me of a former Math teacher that first sparked my interest in Algebra.

[@mutlugundiler4458]

The most intellectual and satisfactory explanation of foundation of this confusing topic. Take away for me is "If you want to understand the foundations of logic, go to a mathematician". Highly appreciated. Thanks. Yet, how can I translate this to a metal detection system operation logic "If metal is detected (P), then set out the alarm (Q)" "If metal then alarm" is TRUE meaning the system is working as designed, "If metal then no alarm" is FALSE meaning that the system is not operating correctly, "If not metal then no alarm" is also TRUE and the system is also working properly, but, "If no metal then alarm" case considered vacuously TRUE confuses me here. It's not true, it's a false alarm, the system is malfunctioning. In electronic design, this case should be assigned "DON'T CARE" value (stay put / remain in the last state). But in logic "don't care" is not truth value. What am I missing to comprehend here?

[@scuzzjumper]

Is it because "don't care" is basically Null and therefore not an equation? I'm just a dullard shooting from the hip...Is it vacuosly true because it is absolutley zero?

[@mauro9180]

It seems that if the original statement was revised to, "*If and only if* metal is detected (P), then set out the alarm (Q)", then the truth value for each case would be the same as before, but the previous flawed case would output FALSE, which is what makes sense in that context.

[@solareclipsedudefinale9026]

Because from ur statement "if metal is detected, then set out the alarm", it doesn't say anything about what happens when no metal is detected; so if no metal is detected, the premise wasn't even true so we aren't even ready to consider whether the whole implication was true since we couldn't get the condition to be met in the first place. And when that happens, as the professor stated, we call it vacuously true.

[@redrose5950]

Very well explained, maintained lecture quality like a Senior Professor.

[@redrose5950]

I m inspired by your tremendous way of delivering lecture. Stay blessed

[@globtier]

Really great , I was really confused before watching ur video. Now my concept is crystal clear. Love u dude.

[@hem4992]

thank you very much. I have finals this week

[@udemy5054]

you just save my life ! i started to learn computer science last month, and your teaching give me a purpose !

[@nikeshasilva2060]

That was super helpful! Your teaching was clear and easy to understand. Thank You!

[@mandwaleadi775]

the biconditional ones had confused a lot. I thought of this example which made a lot of sense to me. If your friend can fly by himself in the sky then you can too. The truth value of it is true

[@Shadowfax2]

My way of understanding is this: The only way the promise p->q is broken is if p is true but q is false. So the negation of p->q is p^~q. But p^~q is true only when p is true and q is false. So p->q is false only when p is true and q is false which explains why the bottom two rows are true for p->q Also the negation of p^~q is ~pvq which is same as p->q as explained in the video

[@icasticasticast]

im a programmer and i was getting really frustrated because this should be a walk in the park for me and I wasn't getting it but turns out It's just an issue of it not "translating" to a language i understand. Really helped when you explained it like hypothesis and conclusion because then I was able to figure out what it means and "translate" it

[@jasonkennedyhernandez4652]

You saved me so much time studying. Everything just clicked.

[@Hooghog]

Another way to think about the truth table with the statement "If you study hard, then you will pass". There are 4 cases: 1) I studied hard and I passed 'You said if I studied hard, then I would pass, and I did! You were right!' the statement is correct [TT->T] 2) I studied hard and I didn't pass 'You said if I studied hard, then I would pass, and I didn't! You were wrong!' the statement is incorrect [TF->F] 3) I didn't study hard and I passed 'I passed! You didn't mention what would happen if I didn't study hard, so for me you're not wrong!' the statement is correct [FT->T] 4) I didn't study hard and I didn't pass 'I didn't pass. You didn't mention what would happen if I didn't study hard, so for me you're not wrong!' the statement is correct [FF->T]

[@jbonceu2457]

Yes alot of people fail to comprehend at first that it's a hypothesis arriving to a conclusion kind of thing. The first statement was just a "guess". If you guessed right, there's no reason to conclude wrong (other wise it doesn't make sense, it's false). And if you guessed wrong, it makes the situation vague, hence any kind of conclusion to that statement makes sense (right)

[@irwansyah1979]

This is the GREAT one

[@borissimovic441]

I have an Intuitive explanation. My statement is: “Whenever I wear a blue jacket then I wear black shoes”. So, in the first row, this statement is true. But in the third row, it is also true, because I didn't say, that I wear black shoes only when I wear a blue jacket but that when I wear a blue jacket I wear black shoes (my point is that black shoes are not a condition for anything, I can wear black shoes with whatever I want, but when I wear a blue jacket then I must wear black shoes, so “blue jacket” is a condition that implies black shoes, and not another way around. This means that I can wear a white jacket and black shoes but the statement:” Whenever I wear a blue jacket then I wear black shoes” doesn't have anything to do with this, it is still true that always when I wear a blue jacket than I must wear black shoes. So this implication is not true only when I do something contradictory to what I claim, for example, I say that: “Whenever I wear a blue jacket then I wear black shoes” and then instead I take some other shoes, for example, I wear a blue jacket but I take some red Nike ✔️. Similarly is for the 4th row. But 2nd the row is the only one that is in contradiction with my statement or claim.

[@loveluz1994]

I’m studying philosophy right now, which is how I came across your video, but this makes so much sense for understanding Stats since I took it last year. My memory is foggy, but this video helps!

[@gracevijay3480]

Tysm! It helped me a lott! God bless you!

[@allenlab4824]

Hello I am from india this question is in my text book your teaching was easily understanding thank you

[@tgcv4444]

This Is An Instant KZbin Classic!

[@Nishh.24s]

This is helpful.. now u r a part of my JEE journey ❤❤

[@vigneshm_rahu]

Great explanation.

[@spencerjames9417]

How do you think about if q then p?

[@satya8997]

p disjunction q similar nagation nagation p conjunction nagation q truth table. Sir please solve the question

[@AnuragGuptainspired]

Somebody please explain for these two statements: p = The weather is sunny q = We will go trekking How can we explain the truth table for p-->q in this case?

[@saityusufbulur3366]

p -> q: If the weather is sunny, we will go trekking. If the weather is sunny and you go trekking (p is true and q is true), you will have fulfilled the promise, that is, the statement will be true. If the weather is sunny but you don't go trekking (p is true but q is false), you break the promise, meaning the statement is false. If the weather is NOT sunny (p is false), the statement is true whether you don't go trekking (q is also false) or you go (q is true). This is because you didn't make any promises about what you would do when the weather is NOT SUNNY. The promise you made was about what you would do if the weather was SUNNY. Therefore, if the weather is NOT SUNNY, your promise has no binding. Think of it this way. Let's say the weather is not sunny and you didn't go trekking, a friend of yours asked, "You said you were going trekking, did you change your mind ?" What answer would you give him ? a. "Yes, I changed my mind." b. "No, I haven't changed my mind. I said I would go when the weather was sunny, but it wasn't sunny, so I didn't go." Your answer will definitely be b, and it will logically satisfy your friend.

[@alanchen6504]

underrated video

[@saityusufbulur3366]

This is how I handle it. Expression p -> q is; - true under all circumstances where p is NOT true - true under all circumstances where q is true If we combine these two ideas, the expression p -> q is true when p is NOT true OR q is true, and we can write it like this: ~p v q Therefore, the expressions p -> q and ~p v q are logically equivalent.

[@mr.rogers9849]

Dude, you had me by 4:30 explaining how conditionals arrive at whether they are true or not.

[@samouflage99]

Thank you so much! When you put the definition there with the type of statement you listed early on, it helped me SO much. One book I'm trying to read for class is not the most organized for this sort of thing.

[@Nisar980]

Dude is very helpful and easy to understand as you teaching visually and we can able understand easily thank you so much and hats off to you for teaching brilliantly.

[@willtg41202]

This was really helpful, but still left me with questions on problems such as “~rv(~p->q)”

[@padraiggluck2980]

Thank you, thank you, thank you! I have been struggling to justify p F and q T and how the implication is T. My text book doesn’t explain and I never heard the phrase ‘vacuously True’ before.⭐️

[@DrTrefor]

Glad it was helpful!

[@RushDefuze]

Took me a few stop and starts, reviewing and writing but when it clicked... amazing thank you!

[@chrishamilton1728]

I think you need to make it clear that the example given was inclusive, meaning that if you don't study hard it is still possible to pass. At first the example seems exclusive, meaning that if you don't study hard, you won't pass, in which case the third column would be false. This caused some confusion for me.

[@adrianbaranowicz507]

Couldn't agree more. I'm surprised people are praising this material despite it being somehow incomplete, hence very confusing.

[@IMAD007VLR]

It is clearly exclusive, you are just not able to comprehend it

[@Jeffkingson]

very good explanation. This is what i were looking for!

[@fromscratch8774]

This one gets everyone, every time.

[@konrad4478]

So that means IF I don’t study hard THEN I will pass the test anyway?

[@astrosky4624]

Actually it's the ~

[@harryb7990]

much better explained than my professor, thanks :)

[@SILVAG831]

You are doing Gods work.

[@aniruddhprakash5583]

Thanks, that was really helpful

[@pingtao8437]

Thanks for your video! I also found it hard to understand until I made this hypothesis: If math works then 2 is an even number. (Math works, so it must be true) If math works then 2 is not an even number. (Math works, then you can't say 2 is not an even number, so it's false) If math doesn't work then 2 is an even number. (Math doesn't work, you can get any conclusion) If math doesn't work then 2 is not an even number. (Math doesn't work, you can get any conclusion)

[@serioustimbersstudychannel4211]

Thanks, very clear and succinct

[@Zen-lz1hc]

Well this was amazing. It starts to make sense. Thank You very much!

[@diya9707]

I wasnt able to wrap my head around why the bottom two rows were interpreted as True until I saw this video, thank you

[@factsbyaditya1308]

thank you sir

[@paulhk2727]

I replayed the last 20s until I understood them, about four times that is. Now I understand, thanks man

[@varunsharma1889]

Very good explanation. I am reading Discrete Maths by Kenneth and was little confused by the explanation there.

[@kopaing7979]

Thank you!!

[@shamasunder969]

I want things on if statements. Nice video

[@tonireyes844]

Sir,, you are BRILLIANT, note please about the subtitle it's HORRIBLE you can do better by fixing this problem Edit: most of the videos have the same problem

[@tonireyes844]

I use English sir .. but I'm not a native speaker that's why I have some problems with it , anyway thank you SIR for infos

[@makermark2159]

Fantastic explanation, thank you

[@hikmattt]

Fantastic video. Just finish a chapter on implications and found your video.

[@anilv9729]

thanks a lot trefor bazett i understood the concept very clearly

[@SriramDinesh]

Really thanks. It's crystal clear now.

[@srijankumaryadav9648]

Sir nice vedio and you are looking like Chris Hemsworth 😃

[@nd685]

You are indeed good looking, professor!

[@mathst6575]

My logic says that they are more vacuously false than true, especially for F=>T=T (I can think about F=>F=F more or less logically, but not about F=>T=T). To me, this does not look like logic but as a purely volitional decision to accept it as true, while it is neither true nor false. And I can't move on until I get it.

[@jbonceu2457]

My thought process for this have always been a hypothesis arriving to a conclusion (p-->q) -If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT) -If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG) -If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT) -If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT) Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)

[@Aakash-yh8ou]

Thank you sir, this makes sense a lot!!

[@jayhun]

this is going to help my valorant career

[@remram4438]

Thank god there's teachers in youtube

[@justinhansen1328]

Thanks for the simple video dude.

[@lableyngtv8629]

Thank you!

[@jaivangordon5966]

8-8 Check

[@SonuSharma-vh5ef]

Incredible 😁 love from India sir❤

[@giantthegreatwonders4236]

You have done it all🙏

[@user-bu8mg7uq3s]

thank you

[@michelesilvestri6484]

American Jack Whitehall is amazing, perfect for visual learners